Horizontal symmetries<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Δ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>150</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Δ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>600</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>
Bibliographic record
Abstract
Using the group theory of mixing to examine all finite subgroups of $SU(3)$ with an order less than 512, we found recently that only the group $\ensuremath{\Delta}(150)$ can give rise to a correct reactor angle ${\ensuremath{\theta}}_{13}$ of neutrino mixing without any free parameters. It predicts ${sin}^{2}2{\ensuremath{\theta}}_{13}=0.11$ and a submaximal atmospheric angle with ${sin}^{2}2{\ensuremath{\theta}}_{23}=0.94$, in good agreement with experiment. The solar angle ${\ensuremath{\theta}}_{12}$, the charge conjugation-parity phase $\ensuremath{\delta}$, and the neutrino masses ${m}_{i}$ are left as free parameters. In this article we provide more details of this case and discuss possible gains and losses by introducing right-handed symmetries and/or valons to construct dynamical models. A simple model is discussed where the solar angle agrees with experiment and all its mixing parameters can be obtained from the group $\ensuremath{\Delta}(600)$ by symmetry alone. The promotion of $\ensuremath{\Delta}(150)$ to $\ensuremath{\Delta}(600)$ is, on one hand, analogous to the promotion of ${S}_{3}$ to ${S}_{4}$ in the presence of tribimaximal mixing, and on the other hand, it is similar to the extension from ${A}_{4}$ to ${S}_{4}$ in that case.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.002 |
| Meta-epidemiology (narrow) | 0.002 | 0.003 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.003 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.000 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; both teacher heads agree on what is shown here.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".